A consumer is observed making two choices. First, he faces prices p = (1,3) with wealthw = 8 but is limited to purchasing no more than 3 units of good 1. Given this budget set, hechooses the bundle x = (2, 2). Second, he faces prices p' = (2,1) and wealth w' = 8 with nolimit on his purchases of either good. Given this budget set, he chooses the bundle 2' = (4,0).dentify all revealed preferences given these choices.Do this consumer's choices satisfy the Weak Axiom of Revealed Preference?- Could these choices result from the consumer choosing optimally given some mono-tone, convex, and continuous preferences? Explain your answer carefully; you do nothave to provide a formal proof.

Since the question you have posted consisted of multiple parts, we will answer the first two…

A consumer is observed making two choices. First, he faces prices p = (1,3) with wealth w = 8 but is limited to purchasing no more than 3 units of good 1. Given this budget set, he chooses the bundle x = (2,2). Second, he faces prices p' = (2, 1) and wealth w' = 8 with no limit on his purchases of either good. Given this budget set, he chooses the bundle x² = (4,0). dentify all revealed preferences given these choices. Do this consumer's choices satisfy the Weak Axiom of Revealed Preference? - Could these choices result from the consumer choosing optimally given some mono- tone, convex, and continuous preferences? Explain your answer carefully; you do not have to provide a formal proof.

A consumer is observed making two choices. First, he faces prices p = (1,3) with wealth w = 8 but is limited to purchasing no more than 3 units of good 1. Given this budget set, he chooses the bundle x = (2,2). Second, he faces prices p' = (2, 1) and wealth w' = 8 with no limit on his purchases of either good. Given this budget set, he chooses the bundle x² = (4,0). dentify all revealed preferences given these choices. Do this consumer's choices satisfy the Weak Axiom of Revealed Preference? - Could these choices result from the consumer choosing optimally given some mono- tone, convex, and continuous preferences? Explain your answer carefully; you do not have to provide a formal proof.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

See similar textbooks

Similar questions

If we observe a consumer choosing (x1, x2) when (y1, y2) is available onetime, are we justified in concluding that (x1, x2) (y1, y2)?
If the consumer thinks that (x₁,x2) is at least as good as (y₁.42) and that (y₁y2) is at least as good as (x₁,x2), we can conclude that (look at the following options)
If Ty's marginal utility for a cup of coffee is 20 and his marginal utility of a donut is 10, then A. they should both be purchased. B. coffee should be his next purchase. C. a donut should be his next purchase. D. price information is also needed to determine what Ty should purchase next.
Vilfredo has complete and transitive preferences on cars. We know that he prefers a Hyundai Sonata to a Mazda 3, and that he finds a Mazda 3 at least as good as a Honda Civic. Can we conclude that he prefers a Hyundai Sonata to a Honda Civic? Yes No
Mats, who has reference-dependent preferences over beer and money, goes to the local pub with a friend, but is not planning on drinking any beer or spending any of his 50 Euro in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively, and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mats’ utility is given by v(6c1 − 6r1) + v(c2 − r2), where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0. (a) Suppose that the price of beer is pB. Calculate Mats’ utility from drinking one pint of beer at this price. What is Mats’ utility from drinking no beer? And, comparing these two utility values, what is the maximum price pB that Mats would pay for one beer? (b) Suppose that Mats unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. [Hint: this means that (r1, r2) = (1, 50).] Suppose that Mats could sell the beer at a price pS.…
1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?
Exercise 2. In order to encourage energy conservation, many public utility companies charge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, a common practice by other firms is to offer “quantity discounts” to consumers who purchase large quantities of a good. Suppose income is $100, PX = $2 if theconsumer buys less than 40 units of X, and PY = $5.A. For the energy case, assume PX = $3 if the consumer buys more than 40 units of XB. For the “quantity discounts” case, assume PX = $1 after 40 units of X were consumed Draw the budget constraints in each of the cases above. What are the implications of the opportunity sets in terms of consumer behavior to consume each of the products?
Suppose Katie buys the bundle (20,9) from the budget line 3x_1 + 5x_2 = 105. When the price of good 1 changes to p1 = 6 and the price of good 2 remains the same, she buys the bundle (5,15). On a later date when p1 = 5 and p2 = 4, by observing Katie’s choices we can say that the Weak Axiom of Revealed Preference (WARP) is violated if a) She buys the bundle (10,15). b) She buys the bundle (15,10) c) She buys the bundle (23,6) d) She buys the bundle (25,25). e) None of the above choices violates WARP.
An agent has income m that can be spent on frequent flier miles f or on other goods – a “composite good” g. Their respective prices are: pf = 10 per mile and pg = 1 per unit. The flier miles have a stepwise price schedule. After the first 25 miles the price is reduced by 20% and after 50 miles the price is further reduced by another 50%.1. Put g on the vertical axis and f on the horizontal axis. Assume m = 200, and draw the budget constraint with all the intercepts and appropriate slopes. 2. On a separate graph, repeat part (1) for m = 300. 3. On a separate graph, repeat part (1) for m = 600.
True/False/Uncertain: 1. In taking an exam, Atack, a rational student, allocates his time to the various questions so as to equalize hismarginal point utility per minute on all questions. 2. The marginal utility of food to Zecher depends only on the amount of food (and not on the amount ofhousing) and the marginal utility declines as more food is consumed; likewise for housing. Therefore,both food and housing are normal goods. (Hint: Express the optimality condition for Zecher’s [UMP], MUF/MUH = PF/PH. Notice that PF/PH is fixed. If all of an increase in income is spent on F, can the equality be maintained?)
f we observe a consumer choosing (x1, x2) when (y1, y2) is available one time, are we justified in concluding that (x1, x2) (y1, y2)?
Consider two treatments. Treatment 1 saves one year of life at a cost of $10,000. Treatment 2 saves ten years of life at a cost of $1,000,000. Which treatment is more cost-effective? Why? Consider two treatments. Treatment 1 saves six years of quality adjusted life at a cost of $90,000. Treatment 2 saves three years of quality adjusted life at a cost of $60,000. Which treatment is preferred from a cost utility analysis perspective? Suppose Jay has been experiencing back pain and that there are two options for back pain: Treatment Regimen Total Cost Pain Reduction Do nothing $0 0 units Cortisone injections $600 30 units Calculate the ICER between cortisone injections and doing nothing. Jay says he is willing to pay $10 for a per unit of pain reduction. Should he choose cortisone injections? Another treatment is discovered. It costs $700 and reduces pain by 25 units. Should he choose the new treatment?